Chemical Kinetics: Elementary Reactions

Shaun Williams, PhD

Reaction Rates

Reaction Rate

The Collision Frequency

Fick's First Law

Equilibrium Constant

Reaction Rates

Microscopic Parameter: Orientation of Reactants

Diagrams of the Importance of the Orientation of Reactants

The steric effect in reaction probability when the chlorine atom is approching the HF molecule such that it will collide with the hydrogen atom so that the reaction occurs. The steric effect in reaction probability when the chlorine atom is approching the (CH3)3CH molecule such that it bounces off without colliding with the hydrogen atom. This means that the reaction does not occur.

Microscopic Parameter: Energy Barrier to Reaction

Macroscopic Parameters



Reaction Velocities

Rate Laws and Complications

Elementary vs Net Reactions

Reaction Mechanisms

Types of Elementary Reactions: Unimolecular

Types of Elementary Reactions: Bimolecular and Termolecular

Simple Collision Theory

Simple Collision Theory

Derivation Summary: Simple Collision Theory

Behavior of the Arrhenius Rate Constant

The value of the Arrhenius constant exponential approaches the value of A as temperature increases.

Example 13.1

Estimate the value of \( A \) in \( \mathrm{cm^3\,mol^{-1}\,s^{-1}} \) for the reaction between oxygen atom and molecular nitrogen, \( \mathrm{O(g) + N_2(g)} \), at \( 298\,\mathrm{K} \). Let the collision cross-section be \( 30\, \AA^2 \) for oxygen and \( 37\, \AA^2 \) for \( \mathrm{N_2} \).

Using the Arrhenius Equation

$$ \begin{align} k & = A \exp \left( -\frac{E_a}{RT} \right) \\ \frac{k}{A} & = \exp \left( -\frac{E_a}{RT} \right) \\ \ln \frac{k}{A} & = -\frac{E_a}{RT} \end{align} $$

First of Two Results in the Derivation

$$ \begin{align} \frac{d}{dT} \left( \ln \frac{k}{A} \right) & = -\frac{d}{dT} \frac{E_a}{RT} \\ \frac{d}{dT} \left( \ln k - \ln A \right) & = \frac{d}{dT} \ln k = -\left( -\frac{E_a}{RT^2} \right) = \frac{E_a}{RT^2} \\ E_a & \equiv RT^2 \frac{d\ln k}{dT} \end{align} $$ This result is great, but experimentally, we needs a more useful approach.

First of Two Results in the Derivation

Let's try a more useful approach $$ \begin{align} \ln \frac{k}{A} & = -\frac{E_a}{RT} \\ \ln k - \ln A & = -\frac{E_a}{RT} \\ \ln k & = -\frac{E_a}{R}\frac{1}{T} + \ln A \end{align} $$ This is now linear. A plot of \( \ln k \) versus \( \frac{1}{T} \) will provide a straight line with a slope of \( -\frac{E_a}{R} \) and a y-intercept of \( \ln A \).

The Arrhenius Plot

If the Arrhenius equation holds, then a graph of the natural log of k versus one over the temperature yields a straight line with a negative slope equal to the negative of the activation energy divided by R.

Example 13.2

For the reaction \( 2NOBr \rightarrow 2NO + Br_2 \), calculate \( k \) at \( 298\,\mathrm{K} \) assuming only the Arrhenius equation (constants given in Table 13.1 of the book). Then predict the values of \( k \) at \( 400\,\mathrm{K} \) if (a) the Arrhenius equation continues to hold and (b) if the Arrhenius value at \( 298\,\mathrm{K} \) is correct but \( A \) is actually of the form \( A' T^\frac{1}{2} \).

Transition State Theory

Transition State Theory

Reaction Diagram for Bimolecular Transition State Theory

A exothermic reaction showing the high energy transition state between the high energy reactants and low energy products A endothermic reaction showing the high energy transition state between the low energy reactants and high energy products

Dividing Surface for \( \mathrm{H+HF} \)

The activated complex may correspond to any geometry along the dividing surface that seperated the reactants from the products.

Eyring Equation

Diffusion-Limited Rate Constants

Diffusion-Limited Rate Constants

Diffusion-Limited Reaction

A sphere of around molecule A is used to approximate the number of other molecules that get close enough to interact with it.

Diffusion Rate

Diffusion-Limited Rate Constant

Rate Laws for Elementary Reactions

Rate Law for Elementary Reactions

Unimolecular Decomposition

First Order Integrated Rate Law

Reaction Half-Life

Concentration Versus Time

Plot of the concentration versus time for a first-order elementary reaction showing the exponential decay and the point at which the concentration is half of its initial value.

Example 13.3

Find the integrated rate law for the elementary reaction \( \mathrm{2A\rightarrow B} \), where \( \mathrm{A} \) is butadiene and \( \mathrm{B} \) is vinylcyclohexene. Use this to obtain an expression for the half-life of butadiene in terms of the rate constant \( k \) and the initial concentration \( \left[ \mathrm{A} \right]_0 \).